freeze.m

nonlinear eq routines in matlab

function varargout = freeze(x)
%
% compute the function value and derivative of 
%   pi*D*h*(T-Tinf)+pi*D*epsilon*sigma*(T^4-Ts^4)-IR
%
%
%
%  [y]    = freeze(x)
%  [y,yp] = freeze(x)  returns the function value in y and 
%                      the derivative in yp
%
%  Matthias Heinkenschloss
%  Department of Computational and Applied Mathematics
%  Rice University
%  April 17, 2001
%

t     =  5184000; % seconds = 60 days
Ti    =  20;      % degree C 
Ts    = -15;      % degree 
alpha = 0.138e-6; %m^2/sec.

% return the function value
varargout{1} = Ts + (Ti - Ts) * erf( x / (2*sqrt(alpha*t)) );
if( nargout > 1 )
  % return the derivative as the second argument
  varargout{2} = (2/sqrt(pi))*(Ti - Ts) ...
                 * exp(-x^2/(4*alpha*t))/(2*sqrt(alpha*t));
end